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%I #21 Jan 25 2023 06:42:20
%S 0,5,10,18,28,40,54,70,88,108,130,154,180,208,238,270,304,340,378,418,
%T 460,504,550,598,648,700,754,810,868,928,990,1054,1120,1188,1258,1330,
%U 1404,1480,1558,1638,1720,1804,1890,1978,2068,2160,2254,2350,2448,2548
%N Zero together with row 4 of the array in A163280.
%H G. C. Greubel, <a href="/A164004/b164004.txt">Table of n, a(n) for n = 0..5000</a>
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3, -3, 1).
%F Conjectures from _Colin Barker_, Apr 07 2015: (Start)
%F a(n) = n*(3+n) = A028552(n) for n > 1.
%F a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n > 4.
%F G.f.: x*(x^3 - 3*x^2 + 5*x - 5) / (x-1)^3. (End)
%F E.g.f.: x*(x+4)*exp(x) + x. - _G. C. Greubel_, Aug 28 2017
%p A033676 := proc(n) local a,d; a := 0 ; for d in numtheory[divisors](n) do if d^2 <= n then a := max(a,d) ; fi; od: a; end: A163280 := proc(n,k) local r,T ; r := 0 ; for T from k^2 by k do if A033676(T) = k then r := r+1 ; if r = n then RETURN(T) ; fi; fi; od: end: A164004 := proc(n) if n = 0 then 0; else A163280(4,n) ; fi; end: seq(A164004(n),n=0..80) ; # _R. J. Mathar_, Aug 09 2009
%t Join[{0, 5}, Table[n*(n + 3), {n, 2, 50}]] (* _G. C. Greubel_, Aug 28 2017 *)
%o (PARI) x='x+O('x^50); concat([0], Vec(x*(x^3 -3*x^2 +5*x -5)/(x-1)^3)) \\ _G. C. Greubel_, Aug 28 2017
%Y Cf. A008578, A161344, A161345, A163280, A164000, A005563, A164005.
%Y Cf. A028552.
%K nonn,easy,less
%O 0,2
%A _Omar E. Pol_, Aug 08 2009
%E Extended beyond a(12) by _R. J. Mathar_, Aug 09 2009
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